True... and I do see how the short division would work well with a single digit divisor and be much faster than long division. I just see it as dangerous to start with the shortcut. The real key being "once you understood division" and I really think that starts with the concrete. Thus, my suggestion in the other thread of base-10 blocks, then going to the standard (long) algorithm. I know it's off subject, but I'm seeing for the first time this semester the results of Everyday Math in my Beginning Algebra class. It's just horrid and I have students who can't do simple arithmetic without the calculator. (Seriously... enough got 1203.34 - 407.83 wrong that I commented on it in class... they don't get place value and how borrowing works - skipped right over the 0 tens and moved 2 hundreds to give 13 ones. OUCH!) So I'm currently very much wanting the standard algorithms right now. :001_huh: :D I've been teaching at the cc level for about 14 years now. I see a lot of students come in with a shaky arithmetic foundation and it's tough getting them the confidence they need and help them move along to algebra. Some days though I do think my students hear me as the teacher from Peanuts. But what's really important to be aware of is that the basic arithmetic skills/procedures/understanding will be used/needed in algebra. The patterns continue when you're working with things other than numbers! (Understanding how to add, subtract, multiply and divide fractions is essential when you're doing the same thing in algebra with rational expressions - and when I have students who only can do fractions with their calculator... they just are dead in the water for algebra.)

In algebra, when you do polynomial division (example here), I don't see how you could do it with "short" division. I had a rough time in calculus because I'd only learned synthetic division (example here) which only works when your divisor is linear with a leading coefficient of 1. It doesn't work when you need to divide by a quadratic for instance. Having a procedure that can be generalized for other topics and expanded is part of the beauty of math. The long division algorithm works for polynomials as well as integers. That's pretty nifty - and pretty powerful. I also think it's better to have a procedure that will work for multiple topics rather than one that works only under certain conditions. (Thus polynomial long division and knowing when synthetic division will work instead of only synthetic division.)

It is taking us I think about 12 months to recoup our closing costs with the refi. Still worth it for us in the long run, but if you're looking to sell in the next year I wouldn't refinance.

We started with a single digit divisor and used base-10 blocks to work through a couple of problems. Then I had my son work the problem with the blocks while I showed him how we'd write it with the algorithm, focusing on place value (we're dividing 8 hundreds into 3 groups. Each group has 2 hundreds. We have 2 hundreds left over, so we break them into tens. We had these tens here, so we now have so many tens. Now we're dividing our tens into 3 groups...). It did take a couple of days to sink in... and we had to go back to the base-10 blocks multiple times. If he tried using the algorithm and got a problem wrong, I'd have him show me with the blocks, then write it out. I really think actually manipulating the blocks makes a huge difference in understanding and I doubt my son would have understood without using the blocks.

Symptoms were just a change in bowel habits (slightly looser) and then a "stripe" of blood on the stool. I had something very similar about a year ago, met with a GI, did an occult blood test that didn't show anything, so stopped there and things went back to normal. This time the blood was more obvious and I went in to my family doctor where an occult test showed blood, so I scheduled the colonoscopy. This time, I think I'd been watching and had the bleeding for a couple weeks (2-3?) and I'd see the blood multiple times in a week. It wasn't completely clear that it was blood sometimes and sometimes it was. I also lost a bit of weight in the past 3 months (only about five pounds but that's about 3% loss without trying). The procedure wasn't bad. I probably still would find it easier than a family visit :) I did a day of a liquid diet and prep was four laxative tablets and two bottles (10 oz) of magnesium citrate. Yukky, but nowhere as bad as other preps! Today they hooked me to an IV and the medicine knocked me out quickly so I remember nothing of the actual procedure. Came home and napped through the afternoon. Dh says the doctor was surprised to find polyps, especially such a large one. Sounds like they were up in the colon but I don't know if it was upper or not. They were easy to remove which is a good sign. He said they could be juvenile polyps (?) or that he also wouldn't be surprised if the "huge" one had precancerous cells. So I'm really glad I had the colonoscopy done (and the doctor said it was very good we did it). I'm feeling fine now- the nap helped. I'm not terribly concerned right now, but I did tell my sister to get a colonoscopy as well (upon the directions of my GI). If this is cancer, we should have caught it early. If it isn't, it's still an early warning sign and I'll be getting another colonoscopy next year. Prayers for the results being benign are appreciated though! :grouphug: And how nifty... This is my first time managing to multiple-quote! :D

So I had two polyps removed - one of them large. I'll be getting biopsy results next week. No hemheroids. Dr said he was really glad we'd done the procedure. So it may still be a good idea to get checked out, Journey.

I'd draw two bars equal in length labeled 150 for the first part. Then take off part from one bar (shading) and add to the other (extend). The difference is 50, so each shaded and extended part is 25. So one group has 175 and the other has 125.

The book I'm thinking of is The Better Part of Valor by Tanya Huff. I enjoyed it, but depending on age, you may want to pre-read. (I'm so pleased I remembered th book!)

I actually have read a book like that. No earthly idea of the title or if it's appropriate for kids.... If I can come up with the title I'll post. I think the book itself would have been written in the 80s or 90s... I'd have read it in the 90s and I think it was a contemporary author (so not pulp days)... Good luck! And there is at least one book out there like that!

And that's where I'm not sure. I know she had bleeding and that was really the only initial symptom. She was only 26 when she was diagnosed - and she thought she just had hemorrhoids. She'd just had her daughter. No family history at all. Only the bleeding and concerns about her daughter not gaining enough weight from nursing. So my prior experience is - rectal bleeding = dead from cancer. I'm very grateful for the nurse who said when scheduling, "It's probably a hemorrhoid." I'm thrilled to hear experiences of people who just had hemorrhoids. That drops the percentages for me (not 100% = cancer). But it's also a good reason to get things checked out. So while I'm not looking forward to prep tomorrow or the check on Friday, I'm looking forward to knowing what's going on. And I'm grateful for hearing of others experiences!

Oh how I love these boards! I'm actually having very similar symptoms (have for a bit) and I'm having my first colonoscopy on Friday as a result. I am hoping for a hemorrhoid. Also no pain, blood on the side, and sometimes bright red. Also no pain. I have a friend (my age) who died of colon cancer at 32, so it's definitely been scary for me. Glad to hear the other stories, hoping all goes well, but it's really nice to know I'm not alone!

I've done just the spoon of honey - no alcohol. It seems to work as well as OTC medicines - and no worries of overmedicating :) OTOH, I thought my son had a cold when he was having an asthma attack, so don't overlook symptoms either. (He ended up on a nebulizer but wasn't admitted to the hospital.)

Iexcel doesn't have nearly as many problems as CWP though. I like the bar models, but it can also be useful to use other methods as well. You (OP) may choose to use other methods to solve the problems but continue to use the CWP books. Nothing requires you to use their method :001_smile:

I have the ones that are one color (mountain climber and bear covers). They are short, but they do a good job of showing the bar models and moving with them from the math sentences to the word problems. If you're ordering something else, you may as well toss in an iExcel to try if you're interested :) Of course, today ds was doing a word problem from CWP, couldn't quite see it without the bar diagram and then threw a major fit when he couldn't see how to draw the bar diagram. :glare: Oh well. Tomorrow's another day. (And he did get the problem once he got the model finally drawn.)

:party:

Here you go... in print :) The demonstration I often give is that if you were going to simplify 12-3^2, your next step would be 12-9 (you certainly wouldn't write 12+9). If the 12 weren't there, you'd have -3^2 = -9. With exponents it's really important to tell what the base is. With -3^2, the base is 3, and you're taking the opposite of it. With -x^2, the base is x, and you're taking the opposite of it (or multiplying by the coefficient, -1). This trips up a lot of people, so it's good to spend enough time and practice now to recognize the difference. Note that some calculators will do the computation correctly and others won't, so be careful with relying on calculators as well.

My son has anaphyllaxis to nuts (and a severe dairy allergy). I have him get the flu shot. When he was 5 and was in the hospital for his anaphylactic reaction, they served him food with dairy. We didn't let him eat anything there. If the flu shot may help keep him out of the hospital,that's what I'm doing since I can't trust them to feed him safely if he's admitted. :glare:

Although if that's a distraction to you, you should let your instructor know about it if there's a no phone policy. Since your school has an honor code, you absolutely should follow the listed procedure. I'm sure it's not easy to do, but it's the right thing to do.

It's from wiki, but here's an explanation of Aristotle's reasoning. Sounds like its explained in his Metaphysics. I don't have a problem with it, although I might not have linked the picture of Jesus as the Prime Mover, but I can understand why artists would have made the connection.

:iagree: McManus can be hysterical. There's the story he tells about his first deer in They Shoot Canoes, Don't They? that used to have me rolling. He was a columnist for Field & Stream, I think. You wouldn't go wrong with any of his books.

If the Everest book was Into Thin Air, then another of Kraukauer's books might be something he'd enjoy. (Eiger Dreams?) Touching the Void is another mountain climbing book, first person. Also very good. Robert B Parker is a really fun author and the books are an easy read... but there's some really neat allusions to catch as well in some of them. He wrote the books that led to the Spencer for Hire tv series in the 80s - and Parker kept writing Spencer books until his death this year. He wrote some Western books that my father has enjoyed: Appaloosa might be fun. Or his Jesse Stone books (first is Night Passage).

I just got Rex Barks. We're using bits of it as a supplement to Practice Island sentences. I do like traditional diagramming and breaking apart the sentence does seem to help my son. He likes the visual of the subject | predicate | direct object I like the structure of diagramming, so that's why we'll do it some over the next few years. I don't think it's essential though.

It's here in the supplemental material for Singapore. Looks like it's being replaced by another program. Glad I've already got the books :) Works well for Gr 1-6. I'm using them with the same level of the Singapore books. They're relatively short supplements & I just add in a topic or two as we need it during the year. So we did the bar models for multiplication and division a couple weeks ago for Bk 3, then we got started with the similar problems in the CWP books.

Unfortunately, it's not necessarily easy. :glare: Sometimes you're stuck with only one professor who teaches the one course you need. Then you get to learn how to suck it up and get the credit. (Also a potentially useful skill.) If you know people you trust who teach at the school, get their off-the-record opinions. Listen to the "talk" around campus from other students. Listen to the reasons students give for liking or disliking a professor. "Love the class; easy A," may be a warning if you're looking for actual learning. I don't think there's much harm with reading RMP although you really have to ignore the ratings, read the comments - reading between the lines, and be aware that you're only getting the students who love or hate the instructor (or in some cases just anyone who knew the instructor... you don't have to have ever taken a course to rate someone).

The students who post on RMP are the ones who either love or hate their instructors. You might get some general ideas about an instructor from it, but I definitely would take any reviews with a shaker of salt. For instance, one of the math instructors at the cc has a lot of really strong reviews on RMP. However, students I get who had him for a prior class are generally in deep trouble. He cancels class regularly, gives take home exams, and doesn't cover all the material a student needs for a subsequent course. Great reviews on RMP for him.... but I'd never let my son take a course from this guy.